1. **State the problem:** Find the present value of an annuity with payments of 1500 every three months for 6 years, with an interest rate of 6% compounded quarterly. 2. **Formula for present value of an ordinary annuity:** $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. 3. **Identify values:** - Payment $P = 1500$ - Annual interest rate = 6% or 0.06 - Compounded quarterly means 4 periods per year - Interest rate per period $r = \frac{0.06}{4} = 0.015$ - Number of years = 6 - Total number of payments $n = 6 \times 4 = 24$ 4. **Calculate present value:** $$PV = 1500 \times \frac{1 - (1 + 0.015)^{-24}}{0.015}$$ 5. Calculate $(1 + 0.015)^{-24}$: $$1 + 0.015 = 1.015$$ $$1.015^{-24} = \frac{1}{1.015^{24}}$$ Calculate $1.015^{24}$: $$1.015^{24} \approx 1.423297$$ So, $$1.015^{-24} = \frac{1}{1.423297} \approx 0.702686$$ 6. Substitute back: $$PV = 1500 \times \frac{1 - 0.702686}{0.015} = 1500 \times \frac{0.297314}{0.015}$$ 7. Simplify fraction: $$\frac{0.297314}{0.015} = 19.820933$$ 8. Multiply by payment: $$PV = 1500 \times 19.820933 = 29731.40$$ **Final answer:** The present value of the annuity is **29731.40**.